On the Representations of the Semisimple Lie Groups. I. The Explicit Construction of Invariants for the Unimodular Unitary Group in N Dimensions

Abstract

It is intended in the present series of papers to discuss explicit constructive determinations of the representations of the semisimple Lie groups SU_n by an extension of the Racah‐Wigner techniques developed for the two‐dimensional unimodular unitary group (SU₂). The present paper defines, and explicitly determines, a symmetric vector‐coupling coefficient for the group SU_n. These coefficients are utilized to construct a series of canonical invariants for SU_n, of which the first I₂ is the familiar Casimir invariant, and it is proved (by construction) that these invariants form a complete system of independent invariants suitable for uniquely labeling the irreducible inequivalent representations of SU_n.